Data Science

Performance anxiety

In our last post, we took a quick look at building a portfolio based on the historical averages method for setting return expectations. Beginning in 1987, we used the first five years of monthly return data to simulate a thousand possible portfolio weights, found the average weights that met our risk-return criteria, and then tested that weighting scheme on two five-year cycles in the future. At the end of the post, we outlined the next steps for analysis among which performance attribution and different rebalancing schemes were but a few.

Portfolio simulations

In our last post, we compared the three most common methods used to set return expectations prior to building a portfolio. Of the three—historical averages, discounted cash flow models, and risk premia models—no single method dominated the others on average annual returns over one, three, and five-year periods. Accuracy improved as the time frame increased. Additionally, aggregating all three methods either by averaging predictions, or creating a multivariate regression from the individual explanatory variables, performed better than two out of the three individual methods.

Discounted expectations

After our little detour into GARCHery, we’re back to discuss capital market expectations. In Mean expectations, we examined using the historical average return to set return expectations when constructing a portfolio. We noted hurdles to this approach due to factors like non-normal distributions, serial correlation, and ultra-wide confidence intervals. While we highlighted these obstacles and offered a few suggestions to counteract such drawbacks, on first blush it didn’t seem like historical averages were all that satisfactory.

Mean expectations

We’re taking a break from our extended analysis of rebalancing to get back to the other salient parts of portfolio construction. We haven’t given up on the deep dive into the merits or drawbacks of rebalancing, but we feel we need to move the discussion along to keep the momentum. This should ultimately tie back to rebalancing, but from a different angle. We’ll now start to examine capital market expectations.

Rebalancing ruminations

Back in the rebalancing saddle! In our last post on rebalancing, we analyzed whether rebalancing over different periods would have any effect on mean or risk-adjusted returns for our three (equal, naive, and risky) portfolios. We found little evidence that returns were much different whether we rebalanced monthly, quarterly, yearly, or not at all. Critically, as an astute reader pointed out, if these had been taxable accounts, the rebalancing would likely have been a drag on performance.

Drawdowns by the data

We’re taking a break from our series on portfolio construction for two reasons: life and the recent market sell-off. Life got in the way of focusing on the next couple of posts on rebalancing. And given the market sell-off we were too busy gamma hedging our convexity exposure, looking for cheap tail risk plays, and trying to figure out when we should go long the inevitable vol crush. Joking. We’re not even sure what any of that means.

Benchmarking the portfolio

In our last post, we looked at one measure of risk-adjusted returns, the Sharpe ratio, to help our hero decide whether he wanted to alter his portfolio allocations. Then, as opposed to finding the maximum return for our hero’s initial level of risk, we broadened the risk parameters and searched for portfolios that would at least offer the same return or better as his current portfolio and would also allow him to find a “comfortable” asset allocation.

SHARPEn your portfolio

In our last post, we started building the intuition around constructing a reasonable portfolio to achieve an acceptable return. The hero of our story had built up a small nest egg and then decided to invest it equally across the three major asset classes: stocks, bonds, and real assets. For that we used three liquid ETFs (SPY, SHY, and GLD) as proxies. But our protagonist was faced with some alternative scenarios offered by his cousin and his co-worker; a Risky portfolio of almost all stocks and a Naive portfolio of 50/50 stocks and bonds.

Skew who?

In our last post on the SKEW index we looked at how good the index was in pricing two standard deviation (2SD) down moves. The answer: not very. But, we conjectured that this poor performance may be due to the fact that it is more accurate at pricing larger moves, which occur with greater frequency relative to the normal distribution in the S&P. In fact, we showed that on a monthly basis, two standard deviation moves in the S&P 500 (the index underlying the SKEW) occur with approximately the same frequency as would be expected in a normal distribution.


The oil-to-gas ratio was recently at its highest level since October 2013, as Middle East saber-rattling and a recovering global economy supported oil, while natural gas remained oversupplied despite entering the major draw season. Even though the ratio has eased in the last week, it remains over one standard deviation above its long-term average. Is now the time to buy chemical stocks leveraged to the ratio? Or is this just another head fake foisted upon unsuspecting generalists unaccustomed to the vagaries of energy volatility?